Entanglement-Enhanced Machine Learning with Quantum Data Acquisition

3. The system of claim 1, further comprising a post-processing module for processing a measurement outcome of the at least one detector to determine a property of the sample.

4. The system of claim 1, the first variational quantum circuit being configured to implement a unitary operation {circumflex over (B)}† to generate the plurality of entangled probe light fields from one or more input light fields, the second variational quantum circuit being configured to implement a unitary operation {circumflex over (B)} to generate the at least one detection light field from the plurality of entangled probe light fields as affected by interaction with the sample, {circumflex over (B)}† being the Hermitian conjugate of {circumflex over (B)}.

5. The system of claim 1, each of the first and second variational quantum circuits comprising a network of one or more beam splitters, one or more phase shifters, or a combination of thereof.

6. The system of claim 1 being a quantum support-vector machine, the first variational quantum circuit being configured to impose a unitary operation {circumflex over (B)}1(w1) on a squeezed vacuum state to generate the plurality of entangled probe light fields, the second variational quantum circuit being configured to impose a unitary operation {circumflex over (B)}2(w2) on the plurality of entangled probe light fields, as affected by interaction with the sample, to generate a plurality of detection light fields, {circumflex over (B)}1(w1) being different from the Hermitian conjugate of {circumflex over (B)}2(w2), w1 being a vector defined by the setting of the first variational quantum circuit, w2 being a vector defined by the setting of the second variational quantum circuit.

10. The system of claim 9, the at least one detector being a detector for measuring the single detection light field, the system further comprising MP detectors for measuring phase properties of the MP entangled output probe light fields to aid a machine learning process to optimize the third and fourth variational quantum circuits.

11. The system of claim 1, the first and second variational quantum circuits implementing a quantum principal-component analyzer for reducing dimensionality of an M-dimensional quantum channel to MP principal components, M and MP being integers, MP<M, the plurality of entangled probe light fields being M entangled probe light fields, the first variational quantum circuit being configured to impose a unitary operation {circumflex over (B)}†(T) on MP squeezed vacuum states to generate the M entangled probe light fields, the second variational quantum circuit being configured to impose a unitary operation {circumflex over (B)}(T) on the M entangled probe light fields, as affected by interaction with the sample, to generate MP detection light fields, {circumflex over (B)}†(T) being the Hermitian conjugate of {circumflex over (B)}(T), T being a transformation defined by the setting of the first and second variational quantum circuits.

12. The system of claim 11, the first variational quantum circuit being configured to generate the plurality of entangled probe light fields as light fields â1′, . . . , âM′, the second variational quantum circuit being configured to generate detection light fields {circumflex over (b)}1′, . . . , {circumflex over (b)}MP′ from the light fields â1′, . . . , âM′, as affected by interaction with the sample, the second variational quantum circuit including MP sequential sub-circuits configured to impose respective unitary transformations {circumflex over (B)}(Tm), m=1, . . . , MP, a first one of the sub-circuits including a plurality of beam splitters and phase shifters for generating light fields {circumflex over (b)}1′, ĉ2′, . . . ĉM′ from the entangled light fields â1′, . . . , âM′, each subsequent one of the sub-circuits including a plurality of beam splitters and phase shifters for generating light fields {circumflex over (b)}m′, ĉm+1′ . . . ĉM′ from light fields ĉm′, ĉm+1′, . . . ĉM′ outputted by a preceding one of the sub-circuits.

13. The system of claim 1, further comprising a plurality of transducers configured to encode information from the sample into the plurality of entangled probe light fields, respectively.

15. The method of claim 14, said optimizing comprising optimizing beam-splitter ratios and phase shifts imposed by the first and second variational quantum circuits.

17. The method of claim 16, the steps of iteratively adjusting and classifying cooperate to minimize a cost function according to a simultaneous perturbation stochastic approximation algorithm.

19. The method of claim 16, further comprising, with a quantum principal-component analyzer between the first and second variational quantum circuits, reducing dimensionality of a quantum channel from M entangled light fields to MP principal components, M and MP being integers, MP<M.

20. The method of claim 19, further comprising, prior to the step of optimizing the setting of first and second variational quantum circuits of the support-vector machine, tuning a setting of a third and fourth variational quantum circuits of the quantum principal-component analyzer to optimize the MP principal components.